\(\left\{\begin{matrix}a_1x+b_2y=c_1 & \\ a_2x+b_2y=c_2 & \end{matrix}\right.\) \(\frac{a_1}{a_2}\neq \frac{b_1}{b_2}\)
\(\left\{\begin{matrix}x=\dfrac{\begin{vmatrix}c_1 & b_1 \\ c_2 & b_2\end{vmatrix}}{\begin{vmatrix}a_1 & b_1\\ a_2 & b_2\end{vmatrix}}=\dfrac{c_1b_2-c_2b_1}{a_1b_2-a_2b_1} & \\ y=\dfrac{\begin{vmatrix}a_1 & c_1 \\ a_2 & c_2\end{vmatrix}}{\begin{vmatrix}a_1 & b_1 \\ a_2 & b_2\end{vmatrix}}=\dfrac{a_1c_2-a_2c_1}{a_1b_2-a_2b_1} & \end{matrix}\right.\)
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